Refer to the graph below. The shaded region represents the solution set of a system of linear inequalities. The system of inequalities is: and and ________.
Answer & Analysis
Analysis
Question Analysis
This question tests the student's ability to identify and write the system of linear inequalities that correspond to a given shaded region on a coordinate plane. The shaded region is bounded by three lines, and the student must recognize the third inequality.
Key Concept Explanation
The key concept here is understanding how to determine the system of inequalities from a graph. The boundary lines are identified, and the nature of each line (solid or dashed) helps in writing the correct inequality.
Step-by-step Solution
1. Identify the boundary lines: , , and .
2. Determine the type of each line:
The first line is solid and the shaded region is above the line, indicating ;
the second line is dashedand the shaded region is below the line, indicating
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